Sadly, I think you are going to have to take her into a vet to have her checked out. If she is really itching she most likely has mites. The safest way to treat mites is with Revolution, which is only available via prescription from your vet.
But lets do a little Q&A.
Any idea how old she is? If she is very young, she may be quilling. Quilling can cause itchiness, dry skin and quill loss. Do you see any new quills poking through her skin?
I'm betting the petstore kept her on a substrate bedding. Any idea what they used? Some beddings can be very irritating to the skin. I once took in an albino that had light grey quills. She was just covered in carefresh dust and was quite filthy. A bath to wash off the substrate may help if the irritation is from that. Usually I like to wait a while before bathing a new hedgehog though, to allow them time to settle down and start to trust me.
Your reaction to her may be that her quills are dirty. However, it is not uncommon for new owners to get a little redness when they first get pricked by quills. Over time many will get used to it. However I still get a little rash if I get quilled and their quills are dirty.
One thing you can do at home to check for mites is to take a black or deep blue piece of cloth, rub her with it until you get some of those skin flakes on it. Then watch for any movement under a bright light. If the skin flakes move, she has mites and definitely needs to see a vet. If they don't move, well she could still have mites, just none fell off.
Does she have any bald spots or spots where the quill coat is quite thin? If yes, this could be a sign of a bad mite infestation. Which means a vet visit is needed as soon as possible.
